A231233 Triangle T(n,k) = greatest prime factor of n*k+1.

2, 3, 5, 2, 7, 5, 5, 3, 13, 17, 3, 11, 2, 7, 13, 7, 13, 19, 5, 31, 37, 2, 5, 11, 29, 3, 43, 5, 3, 17, 5, 11, 41, 7, 19, 13, 5, 19, 7, 37, 23, 11, 2, 73, 41, 11, 7, 31, 41, 17, 61, 71, 3, 13, 101, 3, 23, 17, 5, 7, 67, 13, 89, 5, 37, 61, 13, 5, 37, 7, 61, 73, 17, 97, 109, 11, 19, 29

Offset: 1

Author

Michel Marcus, Nov 06 2013

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  2;
  3,  5;
  2,  7,  5;
  5,  3, 13, 17;
  3, 11,  2,  7, 13;
  7, 13, 19,  5, 31, 37;
  2,  5, 11, 29,  3, 43,  5;
		

Links

• Michel Marcus, Rows n = 1..100 of triangle, flattened
• Étienne Fouvry, On the greatest prime factor of ab+1, arXiv:1311.1161 [math.NT], 2013.

Crossrefs

Cf. A005408, A016777, A016813, A016861, A016921, A016993, A017077, A017173.

Programs

GAP

Flat(List([1..12],n->List([1..n],k->Maximum(FactorsInt(n*k+1))))); # Muniru A Asiru, Sep 23 2018

Mathematica

T[n_, k_] := FactorInteger[n k + 1][[-1, 1]];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 23 2018 *)

PARI

tabl(nn) = {for (n=1, nn, for (k=1, n, f = factor(n*k+1); print1(f[#f~, 1], ", ");); print(););}

Formula

T(n, k) = A006530(n*k+1).